JUNEAU (Reuters) - In family video footage recorded in 1970, a young Senator Mark Begich is seen in a bucolic park catching a ball thrown by his father, a U.S. Congressman from Alaska who died just two years later in a small plane crash en route to Juneau.

"When we were young, our father loved to bring us here, to this spot," Begich says in the campaign commercial four decades later, listing his work to advance oil drilling and gun rights. "When things seem impossible, I try to do what he would have done. I will go anywhere and work with anyone to do what's right for Alaskans."

As Begich fights to retain a vulnerable seat in a close-fought race that could help decide control of the U.S. Senate in the Nov. 4 midterm elections, his campaign has touted his deep roots in Alaska, where he was born and raised, while portraying his Republican challenger Dan Sullivan, who was born in Ohio, as an outsider.

Begich hopes to win over voters who lean toward Republicans but may be open to setting aside labels for a middle-of-the-road candidate whose opinions and experiences are similar to their own, analysts say.

The scion of an Alaska political family, Begich portrays himself as a homegrown power broker fighting for an oil industry whose output from North Slope fields has been long declining and to deliver squadrons of F-35 fighter jets, and the jobs they'd bring, to an Alaska military base.

"What he is saying is, 'I've been here a long time, I've seen it all, I empathize with your situation, I will never let political party stand in the way of what Alaska needs,'" said Jerry McBeath, University of Alaska Fairbanks professor emeritus of politics.

While opinion polls have often been unreliable in Alaska, Begich's strategy, backed by an expansive ground game, could be paying off. According to an average of polls by the website RealClearPolitics, he has narrowed Sullivan's lead to 2.2 percentage points.

VULNERABLE

Republicans need a net gain of six seats to take control of the U.S. Senate, and see Begich as potentially vulnerable.

For his part, Sullivan suggests in one ad that Begich was just "pretending" in a campaign commercial when he rode a snow machine over a patch of Arctic long eyed by the state's oil industry.

In another, Sullivan, an Ivy League-educated Marine reservist, is seen firing a handgun at a television set against a mountain vista, a joking appeal to voters weary of around-the-clock political commercials.

"I have a record that I'm running on. It's a record focused on policies of less government, more freedom," Sullivan, a former Alaska natural resources commissioner and attorney general, told Reuters.

Voters in Republican-leaning Alaska have sent a Democrat to a full Senate term just three times since the early 1970s, but many are seen as persuadable. Some 55 percent of voters identify as independent, although Republicans still outnumber Democrats by nearly 2-to-1, state election records show.

Begich, narrowly elected in 2008 after his then-Republican opponent was convicted of fraud in a verdict that was later vacated, has outspent his challenger at $8.8 million to Sullivan's $6.6 million, according to the Center for Responsive Politics.

In Alaska, candidates traverse thousands of miles - sometimes in a single day - and rely on hundreds of canvassers and staff to win the ground game in a state where a portion of the roughly 500,000 registered voters are spread across vast and often inhospitable territory.

"It's winnable for Begich, but it's still a red (Republican) state. He has to show people how independent he really is," said political analyst Jennifer Duffy of the Cook Political Report.

Begich has trumpeted positions that often align with Republicans, such as on gun rights, fishing for fun and industry, oil and gas, and a balanced budget amendment.

The National Rifle Association, which has endorsed candidates in other key Senate races, said it has withheld support in gun-loving Alaska, torn between Begich's support of liberal Supreme Court justices and his pro-gun voting record.

"In order to fight for Alaska, you have to understand Alaska," Begich wrote in one email to voters days ago. "And if you're an outsider who hasn't spent much time here, it can be tough to really get what the Alaska way of life is all about."

Part of the battle in midterm elections is always getting people to vote, and Begich may also benefit from left-leaning supporters drawn to vote by a ballot measure to legalize recreational marijuana.

Postal carrier Jay Manlulu, who sees daily campaign ads in the mail in Juneau, noted Begich's desire to protect rural post offices from closures. But he remained unsure who to select when he votes for the first time as a U.S. citizen on Nov. 4.

"I think I'm going to support Begich, but it could come down to the last minute," Manlulu said.